From the flexget webui wiki page (http://flexget.com/wiki/Web-UI) you the right way to set the password would be from the command line inside the docker. You can do this by running
docker exec -it FlexGet /bin/bash
from inside either a telnet or ssh session on your unRAID box. This will spawn a bash session inside the docker container and connect you to it. Then you can run the recommended command from the wiki:
flexget web passwd some-password
where some-password is the password you'd like to use. (btw, once you run the /bin/bash command above, you can run the flexget execute -v command)
That's as far as I've gotten. flexget tells me it's updated the password successfully, but the webui still rejects it. Restarting the container still gives me the "no password" error.
UPDATE:
Figured it out. For some reason, my config folder had multiple sqlite databases, so flexget web passwd was updating the wrong one. It's now working as advertised.
Just a heads up for anyone else trying to set the webui password. The command
flexget web passwd some-password
will create/update the db-config.sqlite file located in the current directory, therefore you need to cd to /config first.